In a closed loop air/fuel ratio control system of an internal combustion engine, an air/fuel ratio of a mixture to be delivered to cylinders is controlled in accordance with an output signal of an exhaust gas oxygen sensor (which will be referred to as an O.sub.2 sensor hereinafter) placed in an exhaust system of the engine for measuring oxygen content in the exhaust gas. The O.sub.2 sensor is supplied with a current from a current source and a voltage level of the output signal is considered to be a summation of an electrical potential of the electromotive force and an electrical potential due to a product of the value of an internal resistance and the value of the current supplied thereto. Therefore, the output signal will be referred to as a combined output voltage. Since a sufficient temperature rise is required for the activation of the O.sub.2 sensor, it is general to detect the activation state of the O.sub.2 sensor during the engine starting operation which is initiated by the operation of an ignition switch. By this detection process, it becomes possible to eliminate an operation of the closed loop control system on the basis of a false information of the oxygen content. However, in prior art arrangement, since the detection of activation of the O.sub.2 sensor is performed immediately after the operation of the ignition switch, there was a risk that the O.sub.2 sensor is falsely judged to be activated. This is due to a response characteristic of the control circuit which receives an output signal of the O.sub.2 sensor. More precisely, if the magnitude of the current to be supplied to the O.sub.2 sensor is very small, the product of the value of the internal resistance and the value of the supply current will remain at a low level even though the internal resistance value is still high. In the event such a false discrimination takes place, the closed loop control would be initiated improperly, and in which the air-fuel ratio is controlled irrespectively of the actual oxygen content in the exhausted gas. Such an improper operation of the closed loop control would deteriorate the engine performance, the fuel economy and the emission characteristics.